Title: Correlation functions of higher-dimensional automatic sequences
Authors: BarbĂ©, AndrĂ© ×
von Haeseler, F #
Issue Date: Nov-2004
Publisher: Iop publishing ltd
Series Title: Journal of Physics A. Mathematical and General vol:37 issue:45 pages:10879-10898
Abstract: A procedure for calculating the (auto)correlation function gamma(f) (k), k is an element of Z(m), of an m-dimensional complex-valued automatic sequence f : Z(m) --> C, is presented. This is done by deriving a recursion for the vector correlation function Gamma(ker(f)) (k) whose components are the (cross)correlation functions between all sequences in the finite set ker(f), the so-called kernel of f which contains all properly defined decimations of f. The existence of Gamma(ker(f))(k), which is defined as a limit, for all k is an element of Z(m), is shown to depend only on the existence of Gamma(ker(f)) (0). This is illustrated for the higher-dimensional Thue-Morse, paper folding and Rudin-Shapiro sequences.
ISSN: 0305-4470
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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